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Difference between revisions of "Quadratrix"

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A plane curve used for the solution of the problem of the [[Quadrature of the circle|quadrature of the circle]]. For example: the [[Dinostratus quadratrix|dinostratus quadratrix]], the [[Cochleoid|cochleoid]], the Tschirnhaus quadratrix:
 
A plane curve used for the solution of the problem of the [[Quadrature of the circle|quadrature of the circle]]. For example: the [[Dinostratus quadratrix|dinostratus quadratrix]], the [[Cochleoid|cochleoid]], the Tschirnhaus quadratrix:
  
<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/q/q076/q076160/q0761601.png" /></td> </tr></table>
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$$y=a\sin\frac{\pi x}{2a},$$
  
 
and the Ozanam quadratrix:
 
and the Ozanam quadratrix:
  
<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/q/q076/q076160/q0761602.png" /></td> </tr></table>
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$$x=2a\sin^2\frac{y}{2a}.$$
  
  
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====References====
 
====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  Th.L. Heath,  "A history of Greek mathematics" , '''1–2''' , Dover, reprint  (1981)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  M. Kline,  "Mathematical thought from ancient to modern times" , Oxford Univ. Press  (1972)</TD></TR><TR><TD valign="top">[a3]</TD> <TD valign="top">  B.L. van der Waerden,  "Science awakening" , '''1''' , Noordhoff  (1975)  (Translated from Dutch)</TD></TR><TR><TD valign="top">[a4]</TD> <TD valign="top">  F. Gomes Teixeira,  "Traité des courbes" , '''1–3''' , Chelsea, reprint  (1971)</TD></TR></table>
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<table>
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<TR><TD valign="top">[a1]</TD> <TD valign="top">  Th.L. Heath,  "A history of Greek mathematics" , '''1–2''' , Dover, reprint  (1981)</TD></TR>
 +
<TR><TD valign="top">[a2]</TD> <TD valign="top">  M. Kline,  "Mathematical thought from ancient to modern times" , Oxford Univ. Press  (1972)</TD></TR>
 +
<TR><TD valign="top">[a3]</TD> <TD valign="top">  B.L. van der Waerden,  "Science awakening" , '''1''' , Noordhoff  (1975)  (Translated from Dutch)</TD></TR>
 +
<TR><TD valign="top">[a4]</TD> <TD valign="top">  F. Gomes Teixeira,  "Traité des courbes" , '''1–3''' , Chelsea, reprint  (1971)</TD></TR>
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</table>
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[[Category:Geometry]]

Latest revision as of 18:18, 19 October 2014

A plane curve used for the solution of the problem of the quadrature of the circle. For example: the dinostratus quadratrix, the cochleoid, the Tschirnhaus quadratrix:

$$y=a\sin\frac{\pi x}{2a},$$

and the Ozanam quadratrix:

$$x=2a\sin^2\frac{y}{2a}.$$


Comments

The dinostratus quadratrix is also called the Hippias quadratrix.

References

[a1] Th.L. Heath, "A history of Greek mathematics" , 1–2 , Dover, reprint (1981)
[a2] M. Kline, "Mathematical thought from ancient to modern times" , Oxford Univ. Press (1972)
[a3] B.L. van der Waerden, "Science awakening" , 1 , Noordhoff (1975) (Translated from Dutch)
[a4] F. Gomes Teixeira, "Traité des courbes" , 1–3 , Chelsea, reprint (1971)
How to Cite This Entry:
Quadratrix. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Quadratrix&oldid=11478
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article